Methods and systems for planning evacuation paths

ABSTRACT

Methods and systems for planning evacuation paths are provided to identify an optimum path for evacuation of every evacuee from a region of interest. Methods of the instant disclosure ensure that for each suggested evacuation path, the capacity of any edge on the path is not exceeded and the evacuation time is minimum. A path once identified is maintained. A randomized behavior model is employed to re-distribute evacuees in emergency situations. This provides optimum evacuation time that employs an improved technique with optimized run time and evacuation time after taking into consideration herd behavior.

PRIORITY CLAIM

This U.S. patent application claims priority under 35 U.S.C. § 119 to:India Application No. 3186/MUM/2015 filed on 20 Aug. 2015. The entirecontents of the aforementioned application are incorporated herein byreference.

TECHNICAL FIELD

The embodiments herein generally relate to planning evacuation paths,and more particularly to systems and methods involving probabilisticbehavior models.

BACKGROUND

Evacuation planning is a critical aspect that involves movement ofpeople away from threat or actual occurrence of hazard such as naturaldisasters, terrorist attacks, fires and bombs. Safe evacuation of alarge number of people in a timely manner is a major challenge forbuilding administrators.

There have been several endeavors in this domain to provide methods forplanning evacuation paths. Linear Programming (LP) based polynomial timetechniques for evacuation problem uses time-expanded graphs for thenetwork, where the expression for time complexity makes it non-scalableeven for mid-sized networks. Capacity Constrained Route Planner (CCRP)techniques use generalized shortest path technique to find shortestpaths from any source to any sink, provided that there is enoughcapacity available on all nodes and edges of the path. Space complexityand unnecessary expansion of source nodes in each iteration are two maindisadvantages of CCRP. CCRP++ runs faster than CCRP but the quality ofsolution is not good, because availability along a path may changebetween the times when paths are reserved and when they are actuallyused.

Network flow based approaches are based on minimum cost transshipmentand earliest arrival transshipment. The minimum cost approach does notconsider the distances between evacuees and exits. It may fail if thereare exits very far away. Problems also arise if a lot of exits share thesame bottleneck edges. The earliest arrival approach uses an optimalflow over time and thus does not suffer from these problems. But theexit assignment computed by the earliest arrival approach may not beoptimal.

There is a need therefore for methods and systems that address the aboveand other possible drawbacks and limitations of the currently usedmethods and systems for planning evacuation paths.

SUMMARY

Embodiments of the present disclosure present technological improvementsas solutions to one or more of the above-mentioned technical problemsrecognized by the inventors in conventional systems.

Systems of the present disclosure identify shortest paths from at leastone source to a sink in increasing order of transit time in eachiteration till the transit time of the currently identified path exceedsthe combined evacuation time CET of the previously added set of paths.Also, systems of the present disclosure are not required to identify allpossible paths from a source to a sink; if a path is added in anyiteration, it remains till the end. The combined evacuation time CETafter each iteration will be monotonically non-increasing.

In an emergency, people tend to panic and do not always follow suggestedpaths. To address this issue, system of the present disclosure includesa simple randomized behavior model to obtain a minimum expectedevacuation time.

Methods and systems are described that enable planning of evacuationpaths, in a region of interest, from source nodes to sink nodes in anetwork of routes including a plurality of nodes (n), vertices and edges(E) therebetween.

In an aspect, a computer implemented method of the present disclosureincludes receiving input parameters comprising layouts of the region ofinterest, number of evacuees (p), transit time (T) and maximum capacity(C) associated with each edge (E); defining the network of routes basedon the received input parameters; iteratively performing the steps ofidentifying shortest paths (P) from each source to a sink in increasingorder of transit time associated with the routes constituting thenetwork of routes, eliminating at least one of a node or an edgeassociated with each identified path to obtain a residual network ofroutes, and computing combined evacuation time (CET) and reservecapacity at each of the nodes and edges in the residual network ofroutes, until at least one termination condition is satisfied; andcomputing number of evacuees to be distributed along a each of theidentified paths.

In an embodiment, the method described herein above further includesre-distributing evacuees according to a probabilistic behavioral model.

In an embodiment, the step of computing number of evacuees satisfies therelationship

${{T_{i} + \frac{x_{i}}{C_{i}} - 1} = {C\; E\; T}},$wherein x_(i) is the number of evacuees along path P_(i) having T_(i)transit time and maximum capacity C_(i).

In an embodiment, the step of re-distributing evacuees further includesa step of computing expected evacuation time according to therelationship:

${E\lbrack T\rbrack} = {\max\left( {{T_{1} + \frac{\left( {1 - \alpha} \right)n}{C_{1}} - 1},{\max_{2 \leq i \leq k}\left( {T_{i} + \frac{{\alpha x}_{i}}{C_{i}} - 1} \right)}} \right)}$wherein, E[T] is expected evacuation time, T_(i) is transit time alongPath P_(i), (1−α) is the probability that an evacuee follows theshortest path to the nearest sink, α is the probability that an evacueefollows suggested path, x_(i) is the number of evacuees along path P_(i)and k is the number of identified paths.

In another aspect, there is provided a system for planning evacuationpaths, in a region of interest, from source nodes to sink nodes in anetwork of routes comprising a plurality of nodes (n), vertices andedges (E) therebetween, the system comprising one or more processors; acommunication interface device; one or more internal data storagedevices operatively coupled to the one or more processors for storing:an input module configured to receive input parameters comprisinglayouts of the region of interest, number of evacuees (p), transit time(T) and maximum capacity (C) associated with each edge (E); a networkmodule configured to define the network of routes based on the receivedinput parameters; a path identifier module configured to identifyshortest paths (P) from each source to a sink in increasing order oftransit time associated with the routes; eliminate at least one of anode or an edge associated with each identified path to obtain aresidual network of routes and further configured to compute combinedevacuation time (CET) and reserve capacity at each of the nodes andedges in the residual network of routes; and an evacuee distributingmodule configured to compute number of evacuees to be distributed alongeach of the identified paths.

In an embodiment, the system as described herein above can furthercomprise a path optimizer module configured to re-distribute evacueesaccording to a probabilistic behavioral model.

In yet another aspect, there is provided a computer program product forprocessing data, comprising a non-transitory computer readable mediumhaving program instructions embodied therein for: receiving inputparameters comprising layouts of the region of interest, number ofevacuees (p), transit time (T) and maximum capacity (C) associated witheach edge (E); defining the network of routes based on the receivedinput parameters; iteratively performing the steps of discoveringshortest paths (P) from each source to a sink in increasing order oftransit time associated with the routes, eliminating at least one of anode or an edge associated with each discovered path to obtain aresidual network of routes, and computing combined evacuation time (CET)and reserve capacity at each of the nodes and edges in the residualnetwork of routes, until at least one termination condition issatisfied; computing number of evacuees to be suggested to follow aparticular discovered path; and re-distributing evacuees according to aprobabilistic behavioral model.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments herein will be better understood from the followingdetailed description with reference to the drawings, in which:

FIG. 1 illustrates an exemplary building graph defined on the basis ofinput parameters received by a system of the present disclosure;

FIG. 2 illustrates a portion of an exemplary graph showing parallelflows sent on non edge-disjoint paths;

FIG. 3 illustrates an exemplary block diagram of a system for planningevacuation paths in accordance with an embodiment of the presentdisclosure;

FIG. 4A through FIG. 4B is an exemplary flow diagram illustrating acomputer implemented method for planning evacuation paths using thesystem of FIG. 3 in accordance with an embodiment of the presentdisclosure;

FIG. 5 is a graphical illustration of evacuation time versus number ofnodes for Capacity Constrained Route Planner (CCRP) and Single sourceSingle sink Evacuation Problem (SSEP) of the present disclosure; and

FIG. 6 is a graphical illustration of run time of the technique of thepresent disclosure versus number of nodes for Capacity Constrained RoutePlanner (CCRP) and Single source Single sink Evacuation Problem (SSEP)of the present disclosure.

DETAILED DESCRIPTION

Exemplary embodiments are described with reference to the accompanyingdrawings. In the figures, the left-most digit(s) of a reference numberidentifies the figure in which the reference number first appears.Wherever convenient, the same reference numbers are used throughout thedrawings to refer to the same or like parts. While examples and featuresof disclosed principles are described herein, modifications,adaptations, and other implementations are possible without departingfrom the spirit and scope of the disclosed embodiments. It is intendedthat the following detailed description be considered as exemplary only,with the true scope and spirit being indicated by the following claims.

For ease of explanation, the description of systems and methods of thepresent disclosure is provided with reference to a non-limiting exampleof Single source Single sink Evacuation Problem (SSEP) like evacuatingpeople in an emergency as soon as possible from an auditorium havingonly one exit in the building. It may be understood that systems andmethods of the present disclosure can find applicability in MultipleSource Multiple Sink scenarios with suitable adaptations.

Referring now to the drawings, and more particularly to FIGS. 1 through6, where similar reference characters denote corresponding featuresconsistently throughout the figures, there are shown preferredembodiments and these embodiments are described in the context of thefollowing exemplary system and method.

FIG. 1 illustrates exemplary building graph 100 defined on the basis ofinput parameters received by a system of the present disclosure. Thebuilding floor plan can be represented as a graph G=(V, E), where V andE are the set of vertices and edges respectively. The number of verticesand edges are n and m respectively. Nodes represent rooms, lobbies andintersection points and arcs represent corridors, hallways, staircasesand the like. Some nodes in the building having significant number ofpeople are modeled as source nodes. The exits of a building arerepresented as sink nodes. Each node has a capacity, which is themaximum number of people that can stay at that location at any giventime and an occupancy, which is the number of people currently occupyingthe location. p is the total number of people who needs to be evacuatedor the evacuees.

Each edge has a capacity, which is the maximum number of people that cantraverse the edge per unit time and a travel time, which is the timeneeded to travel from one node to another node along that edge.

The expression “region of interest” as referred to in the presentdisclosure pertains to region or premise of threat or actual occurrenceof hazards such as natural disasters, terrorist attacks, fires andbombs.

The expression “evacuee” as referred to in the present disclosurepertains to people who are intended to be evacuated from the “region ofinterest” as described herein above and may be used interchangeably withthe expression “evacuee” in the context of the present disclosure.

The expression “position detection device” as referred to in the presentdisclosure refers to at least one of sensors, wearable devices, mobiledevices including smartphones, hand-held devices, portable devices andPDAs that can enable detection of location information pertaining to anevacuee. Sensors referred to in this context may be heat sensors, motionsensors or location sensors based on Wi-Fi or any other means known inthe art. Accordingly, in the context of the present disclosure, theexpressions “position detection device” and “sensors” may be usedinterchangeably to refer to device that provides location informationeither directly or indirectly.

Again, expressions used interchangeably throughout the descriptioninclude {graph, network}, {node, vertex}, {edge, arc}, and {path,route}.

The expression “transit time” as referred to in the present disclosurepertains to the sum of the transit times of all the edges in path P fromsource s to sink t, and is denoted as T(P).

The expression “destination arrival time of a path” as referred to inthe present disclosure is the time required by a person to move fromsource s to sink t using path P subject to prior reservations, and isdenoted as DA(P). In other words, DA(P) is the sum of T(P) and anyintermediate delay and DA(P)≥T(P).

The expression “capacity of a path” as referred to in the presentdisclosure pertains to the minimum of the capacities of all nodes andedges present in path P, and is denoted by C(P).

The expression “saturated node or edge” as referred to in the presentdisclosure pertains to a node or edge on a path P when capacity of thatnode or edge is the same as the capacity of path P.

The expression “distinct paths” as referred to in the present disclosurepertains to two paths P₁ and P₂ if and only if V₁≠V₂ or E₁≠E₂, where V₁,V₂ are the set of vertices and E₁, E₂ are the set of edges in the pathsP₁ and P₂ respectively.

Exemplary building graph 100 consists of 10 vertices and 15 edges. Foreach vertex v, its name and the capacity are specified by a pair of theform (v, c(v)). A vertex representing an exit is represented as asquare, while the others are represented as circles. For each edge e,the capacity and the travel time are specified on the edge by the pair(c(e), d(e)). The goal of the system of the present disclosure is tofind the exit and an optimal path (route) for each evacuee, subject tothe constraint that the number of source-sink paths passing through anedge does not exceed the capacity of the edge at any unit time interval.The objective function that the system of the present disclosureminimizes is the total time of evacuation. This is the time at which thelast evacuee is evacuated, hereinafter referred to as the evacuationtime. In an embodiment, system of the present disclosure can minimizetime T in which a feasible flow value at least f can be sent fromsources to sinks.

FIG. 2 illustrates a portion 200 of an exemplary graph showing parallelflows sent on non edge-disjoint paths. In FIG. 2, ordered pair (C, T)denotes capacity and transit time of an edge. There are two paths P₁ andP₂ between source s and sink t.P ₁ :s−B−C−E−G−t,C(P ₁)=4,T(P ₁)=19.P ₂ :s−A−C−E−F−t,C(P ₂)=6,T(P ₂)=23.Paths P₁ and P₂ are not edge-disjoint, but common edge CE has capacityof 10. Accordingly, C(P₁)+C(P₂)=C(CE). So, flow can be sent throughpaths P₁ and P₂ in parallel and edge CE can be considered for allpractical purposes as being two edges one having capacity 4 dedicatedfor P₁ and other one having capacity 6, dedicated for P₂.

The concepts of combined evacuation time (CET) and quickest paths, asknown in the art, consider both transit time and capacity on each pathand provide a fair balance between them. In the event that there are kedge-disjoint paths P1, P2, . . . , Pk from source node s to sink nodet, the combined evacuation time is given by,

$\begin{matrix}{{{CET}\left( {P_{1},\ldots\mspace{11mu},P_{k}} \right)} = \left\lceil \frac{p + {\Sigma_{i = 1}^{k}C_{i}T_{i}}}{\Sigma_{i = 1}^{k}C_{i}} \right\rceil} & (1)\end{matrix}$wherein, C_(i) and T_(i) denote the capacity and transit time of pathP_(i) respectively, and p denotes the number of evacuees. Time requiredto evacuate p people via a path P having transit time T and capacity Cis

$T + \left\lceil \frac{p}{C} \right\rceil - 1.$So, P_(i) is said to be the quickest path in the event that,

${{T_{i} + \left\lceil \frac{p}{C_{i}} \right\rceil - 1} \leq {T_{j} + \left\lceil \frac{p}{C_{j}} \right\rceil - 1}},{\forall{j \in {\left\{ {1,\ldots\mspace{11mu},k} \right\}\backslash\left\{ i \right\}}}}$

The formula for CET, as known in the art, provides an expression forevacuation time and the number of people that will be evacuated on eachpath. It will be understood by those skilled in the art that pathshaving lesser arrival time will evacuate more groups. This technique isknown as QPER (Quickest Path Evacuation Routing). The technique findsall edge-disjoint paths between a single source and a single sink andorders them according to the quickest evacuation time (calculated usingCET) and adds them one by one. The technique does not use time-expandedgraphs and there is no need to store availability information at eachtime stamp, as only edge-disjoint paths are considered. But thetechnique is limited to Single source Single sink Evacuation Problems(SSEP). Also, the addition of paths is not consistent, i.e., a pathadded at some point of time may be removed by the technique at a latterpoint of time, in case removal makes the solution better.

In accordance with the present disclosure, to apply the formula ofcombined evacuation time CET for a set of paths, it is not necessarythat the paths are edge-disjoint, instead the condition is that pathscan be used to send flow in parallel as illustrated in FIG. 2.Conventionally, in an optimal solution of Single Source Sink EvacuationProblem (SSEP), all possible paths between source s and sink t may beused up. In the event that P₁, P₂, . . . , P_(K) are k paths from sources to sink t (not necessarily edge-disjoint), in the worst case k can beexponentially large. But in accordance with the present disclosure, allk paths are not identified at the beginning. Instead paths areidentified one by one in the order of their transit time. Firstly, pathP₁ along with its capacity C₁ having minimum transit time is identifiedand capacities of each node and path of P₁ is decreased by its capacityC₁ permanently to obtain a residual graph. Then path P2 having minimumtransit time in the residual graph is identified and so on. After eachpath addition combined evacuation time CET can be calculated. In anembodiment, a formal technique for the method of the present disclosurecan be as described in Technique 1 herein below.

Input: A graph G (V, E) representing the network with designated sources ϵV and sink t ϵV. Every node v ϵV has an occupancy and maximumcapacity. Every edge e ϵE has a maximum capacity and transit time.Initially, all persons are in s. Output: Evacuation route plan for eachperson. begin  Initialize R = ø and CET = ∞.  Initialize i ← 0.  while(t is reachable from s) and number of discovered paths ≤ p − 1 ≤  doFind the shortest path P_(i+1) from s to t in G (V, E) and let T_(i+1),C_(i+1) be its transit time and capacity respectively.   If T_(i+1) ≤CET then    R = ∪{P_(i+1)}.    CET = CET (S_(i+1)).    Reduce capacityof each node and each edge of P_(i+1) by C_(i+1)    V = V\ {v: v is asaturated node of P_(i+1)).    E = E\ {e: e is a saturated edge ofP_(i+1)}.   end   else    break.   end  end  Let R = {P₁, P₂, . . . ,P_(k)}  Send x_(i) persons via P_(i), 1 ≤ i ≤ k, where  ${T_{i} + \frac{x_{i}}{c_{i}} - 1} = {{CET}.}$ end

Running time analysis of SSEP in accordance with the presentdisclosure—In the event that paths P₁, P₂ . . . P_(K) are identifiedafter execution of Technique 1, as in each step at least one edge or onenode is deleted, at most m+n paths will be identified by system of thepresent disclosure. In each path at least one person will be evacuated.In the worst case, system of the present disclosure can identify ppaths. Hence, k≤min(m+n, p). As each path identification can be done inO(m+n log n) time, Technique 1 requires O(min(m+n,p)(m+n log n)) time.Assuming m=O(n), this becomes O(min(n, p)·n log n), which is always atmost O(pn log n). Time-complexity of CCRP as known in the art is O(pnlog n). Hence. SSEP in accordance with the present disclosure alwaysperforms faster than CCRP. In real life, the number of evacuees is muchlarger than the number of vertices, so SSEP runs much faster than CCRP.

Analysis of Technique 1—Let (P₁, C₁), (P₂, C₂), . . . , (P_(k), C_(k))be distinct paths (not necessarily edge-disjoint) from s to t in orderof their transit time identified by CCRP.

-   -   1. Number of iterations that will return path P_(i) is        T_(k)−T_(i)+ε, 1≤i≤k, where ε denotes number of iterations that        returns path P_(k).    -   2. Number of Iterations that will return path P_(i) before phase        j is T_(j)−T_(i), where i≤j≤k.    -   3. The same paths will be returned by Technique 1.

In accordance with the present disclosure, addition of paths byTechnique 1 of the present disclosure is consistent, i.e. when a path isadded then it will remain till the end of the technique execution.Again, the evacuation time of the solution given by Technique 1 is atmost as that of the CCRP technique for single source and single sink.

In accordance with the present disclosure, upper bound on the evacuationtime given by CCRP (hence by Technique 1) for single source single sinknetwork is

${\left\lfloor \frac{p}{k} \right\rfloor + {\left( {n - 1} \right)\tau} - 1},$where p is the number of evacuees, n is the number of nodes in thegraph, τ is the maximum transit time of any edge and k is the number ofpaths used by CCRP (and Technique 1). Technique 1 also finds a pathafter saturated nodes and edges of all previously identified path aredeleted if it satisfies the conditions given in Technique 1 (linenumbers 4 and 6). Each path identified by CCRP can be represented as anordered pair of path and its group size. Technique 1 also returns a pathwith maximum number of evacuees who can travel by that path at a time.As each path is identified only once in Technique 1, we can alsorepresent each path along with the capacity as an ordered pair. Theabove upper bound is tight. For instance, for a line graph of 10 nodeswhere first node is the source and last node is the sink, if each nodeand edge has capacity of 1 and each edge has a transit time of 10 and inthe event there is only one evacuee, the evacuation time is 90 for p=1,k=1, n=10, τ=10.

In accordance with an embodiment, Technique 1 described herein above canbe extended to the case where there is a single source and multiplesinks. A super sink can be created which is connected to all the sinksof the original graph. The capacity and transit time of all the edges(that connect the super sink to all original sinks) are ∞ and 0respectively.

In an emergency situation, people are stressed and they may considerevacuating via the shortest known path as a better option instead offollowing the route suggested by Technique 1 (or CCRP). This may be dueto several factors like route suggested may not be known by a person,they may feel that suggested path will take longer time to evacuate orthey may display herd behavior wherein when a path is being followed bymajority of people, chances are high that remaining population will alsofollow the same path. Such factors cause the evacuation pattern todeviate from the optimal solution. In an embodiment, systems and methodsof the present disclosure consider probabilistic behavior of people tore-distribute evacuees in an efficient manner.

In the event that in an evacuation, people do not follow paths suggestedby Technique 1 (or CCRP), with probability α>0 that a person followssuggested path and with probability 1−α he follows the shortest path (tothe nearest exit), system of the present disclosure redistributes peoplevia various paths. If x_(i) persons are suggested to follow P_(i), i≠1,then the number of persons of persons who will follow P_(i) and P₁ isαx_(i) and (1−α)x_(i) respectively (in expectation). The total number ofpeople following P₁ and P_(i) are x₁+Σ_(i=2) ^(k)(1−α)x_(i) and αx_(i),i≠1 respectively.

Expected time at which the last person will arrive at destination via P₁is

$T_{1} + \frac{x_{1} + {\sum_{i = 2}^{k}{\left( {1 - \alpha} \right)x_{i}}}}{C_{1}}$Expected time at which last person will arrive at destination via Pi is

${T_{i} + \frac{\alpha\; x_{i}}{C_{i}} - 1},{i \neq 1.}$If the expected evacuation time in this scenario be E[T].

${E\lbrack T\rbrack} = {\max\left( {{T_{1} + \frac{\left( {1 - \alpha} \right)n}{C_{1}} - 1},{\max_{2 \leq i \leq k}\left( {T_{i} + \frac{{\alpha x}_{i}}{C_{i}} - 1} \right)}} \right)}$E[T] will be minimum when it satisfies the following equation,

$\begin{matrix}{{{E\lbrack T\rbrack} = {{T_{1} + \frac{x_{1} + {\sum_{i = 2}^{k}{\left( {1 - \alpha} \right)x_{i}}}}{C_{1}} - 1} = {T_{i} + \frac{\alpha\; x_{i}}{C_{i}} - 1}}},{2 \leq i \leq {k.}},} & (2)\end{matrix}$Where Σ_(i=1) ^(n)x_(i)=n and x_(i)≥0, ∀i. Solving the above equation weget,

$\begin{matrix}{{E\lbrack T\rbrack} = {{\frac{n + {\sum_{i = 1}^{k}{C_{i}T_{i}}}}{\sum_{i = 1}^{k}C_{i}} - 1} = {{CET}\left( \left\{ {P_{1},P_{2},\ldots\mspace{14mu},P_{k}} \right\} \right)}}} & (3)\end{matrix}$Expected evacuation time given by equation (3) doesn't depend on α. Thisis true and solution is feasible as long as x₁≥0. But it is not alwaysthe case, specifically when (1−α) Σ_(i=2) ^(k)x_(i)>C₁(T−T₁+1). So,implicitly evacuation time is dependent on α.

In accordance with an embodiment, on expectation x₁+Σ_(i=2)^(k)(1−α)x_(i)=αx₁+(1−α)n number of people will be evacuated via pathP₁. This is minimum when x₁=0 as x₁≥0. So, lower bound for expectedevacuation time is

${T\; 1} + \frac{\left( {1 - \alpha} \right)n}{C\; 1} - 1.$

In an embodiment, Technique 1 as described herein above can be succeededby a formal technique for re-distributing evacuees as described inTechnique 2 herein below.

-   -   1) Run Technique 1. Find CET and x₁, x₂, . . . , x_(k) using        Equation (2).    -   2) If x₁≥0 then quit; else go to step 3 of Technique 1. In this        case the expected evacuation time=CET.    -   3) Assign x₁′ to 0 and

${x_{i}^{\prime} = \frac{{nx}_{i}}{\sum_{j = 2}^{k}x_{j}}},{\forall{i \neq 1.}}$

-   -    In this case, the expected evacuation time is

$T_{1} + \frac{\left( {1 - \alpha} \right)n}{C_{1}} - 1.$

In accordance with the present disclosure, If x_(i)′ s are calculatedthen x_(i)′<x_(i), ∀i≠1, and Σ_(i=2) ^(n)x_(i)′=n.

In accordance with the present disclosure, Technique 2 has an expectedevacuation time of CET({P₁, P₂, P₃, . . . , P_(k)}) when it quits fromstep-2.

In accordance with the present disclosure, Technique 2 has an expectedevacuation time of

$T_{1} + \frac{\left( {1 - \alpha} \right)n}{C_{1}} - 1$when it quits from step-3.

In accordance with the present disclosure, in SSEP, if evacuees followthe path suggested by Technique 2 with probability α, then the expectedevacuation time is

$\max\left( {{CET},{T_{1} + \frac{\left( {1 - \alpha} \right)n}{C_{1}} - 1}} \right)$and technique runs in O(min(n, p)·n log n) time.

FIG. 3 illustrates an exemplary block diagram of system 300 for planningevacuation paths in accordance with an embodiment of the presentdisclosure and FIG. 4A through FIG. 4B illustrates an exemplary flowdiagram illustrating a computer implemented method 400 for planningevacuation paths using the system of FIG. 3 in accordance with anembodiment of the present disclosure. The steps of method 400 of thepresent disclosure will now be explained with reference to thecomponents of system 300 as depicted in FIG. 3 for planning evacuationpaths, in a region of interest, from source nodes to sink nodes in anetwork of routes including a plurality of nodes (n), vertices and edges(E) therebetween. In an embodiment, system 300 includes one or moreprocessors (not shown), communication interface or input/output (I/O)interface (not shown), and memory or one or more internal data storagedevices (not shown) operatively coupled to the one or more processors.The one or more processors can be implemented as one or moremicroprocessors, microcomputers, microcontrollers, digital signalprocessors, central processing units, state machines, logic circuitries,and/or any devices that manipulate signals based on operationalinstructions. Among other capabilities, the processor(s) is configuredto fetch and execute computer-readable instructions stored in thememory. In an embodiment, system 300 can be implemented on a server orin a variety of computing systems, such as a laptop computer, a desktopcomputer, a notebook, a workstation, a mainframe computer, a server, anetwork server, cloud, hand-held device and the like.

The I/O interface can include a variety of software and hardwareinterfaces, for example, a web interface, a graphical user interface,and the like and can facilitate multiple communications within a widevariety of networks and protocol types, including wired networks, forexample, LAN, cable, etc., and wireless networks, such as WLAN,cellular, or satellite. In an embodiment, the I/O interface can includeone or more ports for connecting a number of devices to one another orto another server.

The memory may include any computer-readable medium known in the artincluding, for example, volatile memory, such as static random accessmemory (SRAM) and dynamic random access memory (DRAM), and/ornon-volatile memory, such as read only memory (ROM), erasableprogrammable ROM, flash memories, hard disks, optical disks, andmagnetic tapes. In an embodiment, the various modules of system 300 canbe stored in the memory.

At step 402, input parameters including layouts of the region ofinterest, number of evacuees (p), transit time (T) and maximum capacity(C) associated with each edge (E) are received at input module 10 ofsystem 100 for planning evacuation paths. In an embodiment, details ofthe region of interest 22 can include layouts of the region of interestas an input to system 100. In an embodiment, position detectiondevice(s) 24 can provide location Information pertaining to each of theevacuees either directly or indirectly to input module 10. In accordancewith an embodiment, system 300 of the present disclosure can betriggered upon receiving an input from one or more hazard detectiondevice(s) 26 to initiate the planning of evacuation paths and computingnumber of evacuees to be suggested to follow a particular path based onmethod 400 of the present disclosure.

At step 404, network module 12 can define a network of routes based onthe received input parameters. In an embodiment, the received inputparameters are defined in the form of a graph as illustrated inexemplary building graph 100 of FIG. 1.

In accordance with an embodiment, path identifier module 14 can beconfigured to identify shortest paths (P) from each source to a sink inincreasing order of transit time associated with the routes at step 406.Further, at step 408, path identifier module 14 can eliminate at leastone of a node or an edge associated with each identified shortest pathto obtain a residual network of routes. Furthermore, at step 410, pathidentifier module 14 can compute combined evacuation time (CET) andreserve capacity at each of the nodes and edges in the residual networkof routes. In an embodiment, path identifier module 14 is furtherconfigured to compute the CET as a function of maximum capacity (C) thetransit time (T) and the number of evacuees (p).

In accordance with an embodiment, termination module 20 checks for atleast one termination condition to be satisfied for terminatingiterative steps 406 through 410. The termination conditions includechecking whether there is a sink node reachable from a source node, thetransit time of identified path is less than combined evacuation time(CET) and whether there is a path identified for each evacuee.

In accordance with an embodiment, evacuee distributing module 16 can beconfigured to compute number of evacuees to be suggested to follow aparticular identified path at step 418 when termination module 20 doesnot detect any of the termination conditions. In an embodiment, evacueedistributing module 16 is further configured to compute the number ofevacuees such that the relationship

${{T_{i} + \frac{x_{i}}{C_{i}} - 1} = {CET}},$is satisfied, wherein x_(i) is the number of evacuees along path P_(i)having T_(i) transit time and maximum capacity C_(i).

In accordance with an embodiment, path optimizer module 18 can beconfigured to re-distribute evacuees according to a probabilisticbehavioral model at step 420. In an embodiment, path optimizer module 18can be further configured to compute the expected evacuation timeaccording to the relationship:

${E\lbrack T\rbrack} = {\max\left( {{T_{1} + \frac{\left( {1 - \alpha} \right)n}{C_{1}} - 1},{\max_{2 \leq i \leq k}\left( {T_{i} + \frac{\alpha\; x_{i}}{C_{i}} - 1} \right)}} \right)}$wherein, E[T] is expected evacuation time, T_(i) is transit time alongPath P_(i), (1−α) is the probability that an evacuee follows theshortest path to the nearest sink, α is the probability that an evacueefollows suggested path, x_(i) is the number of evacuees along path P_(i)and k is the number of identified paths. In an embodiment, the step ofre-distributing evacuees is preceded by the step of receiving locationinformation pertaining to each of the evacuees.

In an embodiment, system 300 can further include annunciator module 30that can be configured to provide at least one of audio and videoannunciations pertaining to suggested identified path for each evacuee.

EXPERIMENTAL RESULTS

The SSEP and CCRP techniques were executed on a Dell Precision T7600server having an Intel Xeon E5-2687 W CPU running at 3.1 GHz with 8cores (16 logical processors) and 128 GB RAM. The operating system wasMicrosoft Windows 7 Professional 64-bit edition. The C/C++ networkanalysis libraries igraph and LEMON

Number Number SSEP (present Improvement in SSEP over of of disclosure)CCRP CCRP (CCRP/SSEP) Nodes Evacuees EVACUATION RUN EVACUATION RUNEVACUATION RUN (n) (p) TIME TIME TIME TIME TIME TIME 100 3000 68 0.12469 1.326 1.01 10.69were used to implement the techniques and netgen was used to generatesynthetic graphs. The number of vertices in the graph varies from 100 to500,000. The number of people varies from 3,000 to 120,000. The resultsare shown in Table I.

TABLE I Comparison between evacuation time and run time between SSEP andCCRP 500 5000 130 0.358 130 2.73 1.00 7.63 1000 7000 155 1.014 15614.586 1.01 14.38 1500 9000 115 1.466 117 35.443 1.02 24.18 2000 15000661 1.622 661 29.016 1.00 17.89 2500 25000 179 2.761 186 25.739 1.049.32 5000 40000 903 3.899 903 93.521 1.00 23.99 10000 65000 517 12.012520 231.535 1.01 19.28 15000 95000 1848 14.025 1853 336.946 1.00 24.0225000 100000 1126 23.134 1128 815.682 1.00 35.26 50000 120000 1436 46.691446 1684.217 1.01 36.07 100000 110000 1032 93.4952 1044 3016.3005 1.0132.26 500000 100000 1698 344.341 1720 11363.253 1.01 33.00

The graphs are plotted on a log-log scale. FIG. 5 is a graphicalillustration of evacuation time versus number of nodes for CCRP and SSEPof the present disclosure and FIG. 6 is a graphical illustration of runtime of the technique of the present disclosure versus number of nodesfor CCRP and SSEP of the present disclosure. From FIG. 5, it can be seenthat the evacuation time of SSEP of the present disclosure is at themost that of CCRP. It is evident from FIG. 6 that the running time ofSSEP of the present disclosure is much lower than that of CCRP. Hence,for all these instances SSEP clearly outperforms CCRP with respect toboth evacuation time and run time. The absolute and relative amount bywhich SSEP performs better than CCRP is shown in Table I herein above.

Although the description is directed towards evacuation from a premise,the invention can be applied suitably to other applications involvingnetwork flow problem including trading, traffic routing, and the like ineither a closed or open region.

The written description describes the subject matter herein to enableany person skilled in the art to make and use the embodiments of theinvention. The scope of the subject matter embodiments defined here mayinclude other modifications that occur to those skilled in the art. Suchother modifications are intended to be within the scope if they havesimilar elements that do not differ from the literal language of theclaims or if they include equivalent elements with insubstantialdifferences from the literal language.

It is, however to be understood that the scope of the protection isextended to such a program and in addition to a computer-readable meanshaving a message therein; such computer-readable storage means containprogram-code means for implementation of one or more steps of themethod, when the program runs on a server or mobile device or anysuitable programmable device. The hardware device can be any kind ofdevice which can be programmed including e.g. any kind of computer likea server or a personal computer, or the like, or any combinationthereof. The device may also include means which could be e.g. hardwaremeans like e.g. an application-specific integrated circuit (ASIC), afield-programmable gate array (FPGA), or a combination of hardware andsoftware means, e.g. an ASIC and an FPGA, or at least one microprocessorand at least one memory with software modules located therein. Thus, themeans can include both hardware means and software means. The methodembodiments described herein could be implemented in hardware andsoftware. The device may also include software means. Alternatively, theinvention may be implemented on different hardware devices, e.g. using aplurality of CPUs.

The embodiments herein can comprise hardware and software elements. Theembodiments that are implemented in software include but are not limitedto, firmware, resident software, microcode, etc. The functions performedby various modules comprising the system of the present disclosure anddescribed herein may be implemented in other modules or combinations ofother modules. For the purposes of this description, a computer-usableor computer readable medium can be any apparatus that can comprise,store, communicate, propagate, or transport the program for use by or inconnection with the instruction execution system, apparatus, or device.The various modules described herein may be implemented as eithersoftware and/or hardware modules and may be stored in any type ofnon-transitory computer readable medium or other storage device. Somenon-limiting examples of non-transitory computer-readable media includeCDs, DVDs, BLU-RAY, flash memory, and hard disk drives.

A data processing system suitable for storing and/or executing programcode will include at least one processor coupled directly or indirectlyto memory elements through a system bus. The memory elements can includelocal memory employed during actual execution of the program code, bulkstorage, and cache memories which provide temporary storage of at leastsome program code in order to reduce the number of times code must beretrieved from bulk storage during execution.

Further, although process steps, method steps, techniques or the likemay be described in a sequential order, such processes, methods andtechniques may be configured to work in alternate orders. In otherwords, any sequence or order of steps that may be described does notnecessarily indicate a requirement that the steps be performed in thatorder. The steps of processes described herein may be performed in anyorder practical. Further, some steps may be performed simultaneously.

The illustrated steps are set out to explain the exemplary embodimentsshown, and it should be anticipated that ongoing technologicaldevelopment will change the manner in which particular functions areperformed. These examples are presented herein for purposes ofillustration, and not limitation. Further, the boundaries of thefunctional building blocks have been arbitrarily defined herein for theconvenience of the description. Alternative boundaries can be defined solong as the specified functions and relationships thereof areappropriately performed. Alternatives (including equivalents,extensions, variations, deviations, etc., of those described herein)will be apparent to persons skilled in the relevant art(s) based on theteachings contained herein. Such alternatives fall within the scope andspirit of the disclosed embodiments. Also, the words “comprising,”“having,” “containing,” and “including,” and other similar forms areintended to be equivalent in meaning and be open ended in that an itemor items following any one of these words is not meant to be anexhaustive listing of such item or items, or meant to be limited to onlythe listed item or items. It must also be noted that as used herein andin the appended claims, the singular forms “a,” “an,” and “the” includeplural references unless the context clearly dictates otherwise.

It is intended that the disclosure and examples be considered asexemplary only, with a true scope and spirit of disclosed embodimentsbeing indicated by the following claims.

What is claimed is:
 1. A computer implemented method for planningevacuation paths, in a region of interest, from source nodes to sinknodes in a network of routes comprising a plurality of nodes (n),vertices and edges (E) there between, said method comprising: (a)receiving input parameters comprising layouts of the region of interest,number of evacuees (p), transit time (T) and maximum capacity (C)associated with each edge (E); (b) defining the network of routes basedon the received input parameters; (c) identifying shortest paths (P)from each source to a sink in increasing order of transit timeassociated with the routes constituting the network of routes; (d)eliminating at least one of a node or an edge associated with eachidentified shortest path to obtain a residual network of routes; (e)computing combined evacuation time (CET) and reserve capacity at each ofthe nodes and edges in the residual network of routes; (f) iterativelyperforming steps (c) through (e) until at least one condition of (i)there is a sink node reachable from a source node; (ii) the transit timeof identified shortest path is less than combined evacuation time (CET);and (iii) there is a path identified for each evacuee; is satisfied; and(g) computing number of evacuees to be distributed along each of theidentified paths, further wherein computing number of evacuees satisfiesa relationship T i+x i C i−1=CET wherein xi is the number of evacueesalong path Pi having Ti transit time and maximum capacity Ci.
 2. Thecomputer implemented method of claim 1, further comprisingre-distributing evacuees according to a probabilistic behavioral model.3. The computer implemented method of claim 1, wherein the step ofdefining the network of routes includes defining the received inputparameters in the form of a graph.
 4. The computer implemented method ofclaim 1, wherein the CET is a function of maximum capacity (C), thetransit time (T) and the number of evacuees (p).
 5. The computerimplemented method of claim 1, wherein the step of computing number ofevacuees satisfies a relationship that is based on the number ofevacuees xi along path Pi having Ti transit time and maximum capacityCi.
 6. The computer implemented method of claim 2, wherein the step ofre-distributing evacuees further comprises a step of computing expectedevacuation time satisfies a relationship based on transit time Ti alongPath Pi, probability that an evacuee follows the shortest path to thenearest sink (1−α), probability that an evacuee follows suggested pathα, number of evacuees xi along path Pi and number of identified paths k.7. The computer implemented method of claim 2, wherein the step ofre-distributing evacuees further comprises a step of computing expectedevacuation time according to a relationship:E□[T]=max□(T1+(1−α)□nC1−1,max2≤i≤k□(Ti+α□□xi Ci−1)) wherein, E[T] isexpected evacuation time, Ti is transit time along Path Pi, (1−α) is theprobability that an evacuee follows the shortest path to the nearestsink, α is the probability that an evacuee follows suggested path, xi isthe number of evacuees along path Pi and k is the number of identifiedpaths.
 8. The computer implemented method of claim 2, wherein the stepof re-distributing evacuees is preceded by the step of receivinglocation information pertaining to each of the evacuees.
 9. A system forplanning evacuation paths, in a region of interest, from source nodes tosink nodes in a network of routes comprising a plurality of nodes (n),vertices and edges (E) there between, said system comprising: one ormore processors; a communication interface device; one or more internaldata storage devices operatively coupled to the one or more processorsfor storing: an input module (10) configured to receive input parameterscomprising layouts of the region of interest, number of evacuees (p),transit time (T) and maximum capacity (C) associated with each edge (E);a network module (12) configured to define the network of routes basedon the received input parameters; a path identifier module (14)configured to identify shortest paths (P) from each source to a sink inincreasing order of transit time associated with the routes; eliminateat least one of a node or an edge associated with each identifiedshortest path to obtain a residual network of routes and furtherconfigured to compute combined evacuation time (CET) and reservecapacity at each of the nodes and edges in the residual network ofroutes; and an evacuee distributing module (16) configured to computenumber of evacuees to be distributed along each of the identified paths,wherein the evacuee distributing module (16) is further configured tocompute the number of evacuees such that a relationshipTi+xiCi−1=CET, is satisfied, wherein xi is the number of evacuees alongpath Pi having transit time Ti and maximum capacity Ci.
 10. The systemof claim 9, further comprising a path optimizer module (18) configuredto re-distribute evacuees according to a probabilistic behavioral model.11. The system of claim 9, wherein the input module (10) is furtherconfigured to receive location information pertaining to each of theevacuees from at least one sensor configured to detect location of theevacuees either directly or indirectly.
 12. The system of claim 9,wherein the network module (12) is further configured to define thereceived input parameters in the form of a graph.
 13. The system ofclaim 9, wherein the path identifier module (14) is further configuredto compute the CET as a function of maximum capacity (C) the transittime (T) and the number of evacuees (p).
 14. The system of claim 9,wherein the evacuee distributing module (16) is further configured tocompute the number of evacuees such that a relationship that is based onthe number of evacuees xi along path Pi having Ti transit time andmaximum capacity Ci is satisfied.
 15. The system of claim 10, whereinthe path optimizer module (18) is further configured to compute expectedevacuation time satisfies a relationship based on transit time Ti alongPath Pi, probability that an evacuee follows the shortest path to thenearest sink (1−α), probability that an evacuee follows suggested pathα, number of evacuees xi along path Pi and number of identified paths k.16. The system of claim 10, wherein the path optimizer module (18) isfurther configured to compute expected evacuation time according to arelationship:E□[T]=max□(T1+(1−α)□nC1−1,max2≤i≤k□(Ti+α□□xiCi−1)) wherein, E[T] isexpected evacuation time, Ti is transit time along Path Pi, (1−α) is theprobability that an evacuee follows the shortest path to the nearestsink, α is the probability that an evacuee follows suggested path, xi isthe number of evacuees along path Pi and k is the number of identifiedpaths.
 17. The system of claim 9, further comprising one or more of: atermination module (20) configured to check for at least one terminationcondition selected from the group consisting of: (a) there is a sinknode reachable from a source node; (b) the transit time of identifiedpath is less than combined evacuation time (CET); and (c) there is apath identified for each evacuee; and an annunciator module (301)configured to provide at least one of audio and video annunciationspertaining to suggested identified path for each evacuee.